Here is a picture of the actual squash, and I have plenty!
Last year I ordered the same variety from a reputable company, and they were long with the ball shape on the end just like your photo. I let them stay on the vine until they turned gold, like a winter squash, and thought they were very good. They got over 2 ft long, and the neck part had no seeds, so they were easy to prepare. I think you got the right squash, but picked too early...they are not a zuccinni type. I saved some seeds and am trying again this year.
Just out of curiosity: did all the plants survive the vine borers?
Just a follow up...
After trying to cook with very young squash from this mysterious plant and finding it not tasty,and also tasting some true tromboncino that I had in my garden and finding those delicious, I yanked out all of the mystery squash vines.
Let me tell you, this was a project.. The vines were extremely tough and I saw no evidence of SVB, nor squash bugs. The main vines from which the squash grow off were very hard, and had rooted themselves into the ground with some tenacity. I was surprised. Even though this was obviously a hybrid of tromboncino and something else, whatever tromboncino genes were still in that plant were no joke. I used my brand new Fiskar clippers to cut these vine apart and loosen them from the ground, and after a while, those clippers started to struggle to cut the vines.
I had about 20 mystery squash that I cut to reveal the seeds for the birds and then put on the compost pile.
Meanwhile, my other "true" tromboncino plants are doing well, no bugs yet but some brave deer have developed a taste for them an are attacking those plants.
If it isn't one thing, it's another...